This research proposes to develop fast expectation-maximization (EM) algorithms for 3D reconstruction of high resolution reconstruction of small particles in Cryogenic Electron Microscopy (Cryo-EM). The proposed algorithm incorporates the contrast transfer function (CTF) of the microscope and can be used with any basis functions. Further, two strategies are proposed to speed up the algorithm by a factor of 1000. The two strategies are (1) domain reduction where the E step of the algorithm is sped up, and (2) implementation on commodity graphics cards, where the massive parallelism of the graphics processors speeds up the entire algorithm. Preliminary results using simulations based on ribosome and the IP3R Ca+ channel protein structure show that the E and M steps of the proposed algorithm are fast and accurate. The proposed research extends previous work by (1) further developing the domain reduction strategy into a multi-resolution strategy, (2) systematically parallelizing the M step, and (3) implementing and validating the complete algorithm. Further, systematic software design is planned for implementing the algorithm on graphics processor units. This software will be made available on the world-wide web for other researchers. The algorithm will be validated using simulations and real-world Cryo-EM images. The reconstruction accuracy will be measured by the average mean squared error in reconstruction, and the resolution will be measured by Fourier shell correlation. The accuracy will also be compared to the reconstruction accuracy of conventional algorithms. The speed of the algorithm will be measured as a function of number of images and signal to noise ratio.